Extended Tolerance Relation to Define a New Rough Set Model in Incomplete Information Systems

This paper discusses and proposes a rough set model for an incomplete information system, which defines an extended tolerance relation using frequency of attribute values in such a system. It first discusses some rough set extensions in incomplete information systems. Next, “probability of matching” is defined from data in information systems and then measures the degree of tolerance. Consequently, a rough set model is developed using a tolerance relation defined with a threshold. The paper discusses the mathematical properties of the newly developed rough set model and also introduces a method to derive reducts and the core

Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the terminology of linear algebra and graph theory. We can combine rough set theory with matroid theory through using rough sets to study some characteristics of matroids. In this paper, we apply rough sets to matroids through defining a family of sets which are constructed from the upper approximation operator with respect to an equivalence relation. First, we prove the family of sets satisfies the support set axioms of matroids, and then we obtain a matroid. We say the matroids induced by the equivalence relation and a type of matroid, namely support matroid, is induced. Second, through rough sets, some characteristics of matroids such as independent sets, support sets, bases, hyperplanes and closed sets are investigated.Comment: 13 page

Covering rough sets based on neighborhoods: An approach without using neighborhoods

Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin

A Comparative Analysis of Rough Sets for Incomplete Information System in Student Dataset

Rough set theory is a mathematical model for dealing with the vague, imprecise, and uncertain knowledge that has been successfully used to handle incomplete information system. Since we know that in fact, in the real-world problems, it is regular to find conditions where the user is not able to provide all the necessary preference values. In this paper, we compare the performance accuracy of the extension of rough set theory, i.e. Tolerance Relation, Limited Tolerance Relation, Non-Symmetric Similarity Relation and New Limited Tolerance Relation of Rough Sets for handling incomplete information system in real-world student dataset. Based on the results, it is shown that New Limited Tolerance Relation of Rough Sets has outperformed the previous techniques.

A relative tolerance relation of rough set in incomplete information

University is an educational institution that has objectives to increase student retention and also to make sure students graduate on time. Student learning performance can be predicted using data mining techniques e.g. the application of finding essential association rules on student learning base on demographic data by the university in order to achieve these objectives. However, the complete data i.e. the dataset without missing values to generate interesting rules for the detection system, is the key requirement for any mining technique. Furthermore, it is problematic to capture complete information from the nature of student data, due to high computational time to scan the datasets. To overcome these problems, this paper introduces a relative tolerance relation of rough set (RTRS). The novelty of RTRS is that, unlike previous rough set approaches that use tolerance relation, non-symmetric similarity relation, and limited tolerance relation, it is based on limited tolerance relation by taking account into consideration the relatively precision between two objects and therefore this is the first work that uses relatively precision. Moreover, this paper presents the mathematical properties of the RTRS approach and compares the performance and the existing approaches by using real-world student dataset for classifying university’s student performance. The results show that the proposed approach outperformed the existing approaches in terms of computational time and accuracy